n Let S := 1 ² ² + 1 =nEN } . n²+1 f S. Fully justify your answers! Prove that S is bounded and determine sup S and

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: Let X~Bin(10, 0.3). What is P(X<2)?

A:

Q: Po fo 22 PE 1(1234)=PP 13)29 pz pz (1432) = p3 p3 pir %3D 12)(34) = E to C13) = pE PE For each…

A: Group D4 is the group of symmetries of the square. Through various rotations, set D4 is formed. In…

Q: Theorem 8. i) Every solution of Eq.(2) is bounded from above such that xo #0, x-1#0 and a > 0 min(,)…

A: Given : Equation (2)               xn+1=xnxn2+α where x02≠-α. To prove : Theorem 8, part (i)

Q: Let S be a closed n-cube with v(S) > 0. Suppose g, h : S → R are two bounded #3 and integrable…

A:

Q: 10) tind tre area of tve region boonded by the Graphs Of tre Given functions y- 2-x* ,4= 2-4X The…

A:

Q: Let Z~ N(0, 1). Find P( - 2.4 < Z < 0.9). Submit Question

A: Solution-: In this case, Z is the standard normal random variable with μ=0 and σ=1. Mathematically,…

Q: - A = {1²³ = 11 € N₂₁ +1}. : - Let B be a bounded from above subset of R. Prove that -B + A is…

A:

Q: Use the Error Bound to find a value of N for which error (TN) ≤ 10. Let K₂ be the maximum of If"(x)]…

A: Given ∫257xdx, We have to calculate N by using error bound.

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

A:

Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

A:

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 10) Calculate a lower sum for f(x) = 2x + 5 over the interval [0, 2] using 4 rectangles. %3D

A:

Q: Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

A:

Q: Let Z ~ N(0, 1). Find P(Z > 1).

A: Z~N(0,1). This implies that Z is a Standard Normal Random Variable. The PDF of Z is given by,

Q: 3) √³/₂2 5 - dx -2 2x-1

A: